Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions
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Authors
Ting-Song Du
- College of Science, China Three Gorges University, 443002, Yichang, P. R. China.
- Hubei Province Key Laboratory of System Science in Metallurgical Process, Wuhan University of Science and Technology, 430081, Wuhan, P. R. China.
Jia-Gen Liao
- College of Science, China Three Gorges University, 443002, Yichang, P. R. China.
Yu-Jiao Li
- College of Science, China Three Gorges University, 443002, Yichang, P. R. China.
Abstract
The authors introduce the concepts of m-invex set, generalized \((s,m)\)-preinvex function, and explicitly
\((s,m)\)-preinvex function, provide some properties for the newly introduced functions, and establish new
Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first
derivative is generalized \((s,m)\)-preinvex function. By taking different values of the parameters, Hadamardtype
and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special
case present a refinement and improvement of previously known results.
Share and Cite
ISRP Style
Ting-Song Du, Jia-Gen Liao, Yu-Jiao Li, Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3112--3126
AMA Style
Du Ting-Song, Liao Jia-Gen, Li Yu-Jiao, Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions. J. Nonlinear Sci. Appl. (2016); 9(5):3112--3126
Chicago/Turabian Style
Du, Ting-Song, Liao, Jia-Gen, Li, Yu-Jiao. "Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3112--3126
Keywords
- Integral inequalities of Hadamard-Simpson type
- Hölder's inequality
- \((s،m)\)-preinvex function.
MSC
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